Question

What are the extrema and saddle points of `f(x,y) = x^2y+y^3x -1/x^3 + 1/(xy^2)`?

Answer 1

See the answer below:

Explanation:

1.Thanks to the free software that supported us with the graphics.
https://www.geogebra.org/

2.Thanks to the web site WolframAlpha who gave us numeric aproximate solution of the system with implicit functions.
http://www.wolframalpha.com/